Factorized scattering in the presence of reflecting boundaries

Fring, Andreas; Köberle, R.

doi:10.1016/0550-3213(94)90229-1

Cited by 110 publications

(153 citation statements)

References 22 publications

(23 reference statements)

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“…Further studies regarding the boundary ATFT at both classical and quantum level may be also found in various articles (see e.g. [13]- [18]). …”

Section: Introductionmentioning

confidence: 99%

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

Doikou¹

2008

J. High Energy Phys.

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Generic classically integrable boundary conditions for the A (1) n affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A (1) 2 ATFT, however our results may be generalized for any A (1) n (n > 1). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the (q) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motions for SP boundary conditions is 'double' compared to those of the SNP case.

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“…Further studies regarding the boundary ATFT at both classical and quantum level may be also found in various articles (see e.g. [13]- [18]). …”

Section: Introductionmentioning

confidence: 99%

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

Doikou¹

2008

J. High Energy Phys.

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“…The same spectrum can be obtained using the completely different approach of the bootstrap method. It is based on the pioneering work of Cherednik [21], Ghoshal and Zamolodchickov [9], and Fring and Köberle [22]. This way we shall be able to compare and compliment the results to acquire an even more accurate spectrum.…”

Section: The Bootstrap Methodsmentioning

confidence: 99%

Quantum complex sine-Gordon model on a half line

Bowcock

Tzamtzis

2007

J. High Energy Phys.

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In this paper, we examine the quantum complex sine-Gordon model on a half line. We obtain the quantum spectrum of boundary bound states using the the semiclassical method of Dashen, Hasslacher and Neveu. The results are compared and found to agree with the bootstrap programme. A particle/soliton reflection factor is conjectured, which is consistent with unitary, crossing and our semi-classical results.

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“…They can be derived most easily simply by exploiting the associativity of the so-called Zamolodchikov-Faddeev (ZF) algebra [21] and its extended version which includes an additional generator representing a boundary [22,23,24] or a defect [25,26]. Indicating particle types by Latin and degrees of freedom of the impurity by Greek letters, the "braiding" (exchange) relations of annihilation operators Z i (θ) of a particle of type i moving with rapidity θ and defect operators Z α in the state α can be written as…”

Section: Defect Yang-baxter Equationsmentioning

confidence: 99%

From integrability to conductance, impurity systems

Castro-Alvaredo

Fring

2003

Nuclear Physics B

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We compute the DC conductance with two different methods, which both exploit the integrability of the theories under consideration. On one hand we determine the conductance through a defect by means of the thermodynamic Bethe ansatz and standard relativistic potential scattering theory based on a Landauer transport theory picture. On the other hand we propose a Kubo formula for a defect system and evaluate the currentcurrent two-point correlation function it involves with the help of a form factor expansion. For a variety of defects in a fermionic system we find excellent agreement between the two different theoretical descriptions.

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Factorized scattering in the presence of reflecting boundaries

Cited by 110 publications

References 22 publications

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

Quantum complex sine-Gordon model on a half line

From integrability to conductance, impurity systems

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Factorized scattering in the presence of reflecting boundaries

Cited by 110 publications

References 22 publications

An(1)affine Toda field theories with integrable boundary conditions revisited

An(1)affine Toda field theories with integrable boundary conditions revisited

Quantum complex sine-Gordon model on a half line

From integrability to conductance, impurity systems

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Product

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A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited